[magistral (OP)]

I have two toroidal permanent magnets which are fitted over
magnet.jpg (151.11 kB . 805x989 - viewed 2329 times)
magnet.jpg (151.11 kB . 805x989 - viewed 2329 times)a plastic tube with like poles facing each other.
Because of the magnetic repulsion the top magnet 'hovers' 20mm above the bottom one. I have had this pair
of magnets as an ornament in my workshop for more than 10 years and there is no discernable change in the
gap between them. The magnets are about 85mm in diameter, the central hole of the toroid about 50mm and they
weigh about 400g each.

My question is:
Where does the energy come from to support the top magnet against the force of gravity. Classical Physics seems to say that with the magnets in this static situation then no energy is involved and no work is done as
there is no movement or displacement. However, If I push the top magnet towards the lower one and release it, it
returns to it's 'hover' position. Clearly energy is required to do that. No matter how many times that is done, the permanent magnetism does not seem to be depleted.

As a thought experiment, if the bottom magnet was replaced with an electromagnet then electrical energy would be required to support the top magnet and if the power was removed the top magnet would drop. I realise that toroidal electromagnets have no external magnetic field but if bar magnets were used instead and constrained horizontally in a tube then the same would apply.

[Bored chemist]

"where does permanent magnet energy come from"
You.

However, If I push the top magnet towards the lower one

[evan_au]

where does permanent magnet energy come from...If I push the top magnet towards the lower one

You just answered the question.

Pushing the top magnet down against the repulsion of the lower magnet requires a force F.
This is applied over a distance s.
The product of Force an distance = Energy: Fs=E

This is just the same as if you had compressed a spring and released it.

if the bottom magnet was replaced with an electromagnet then electrical energy would be required to support the top magnet

Not if the electromagnet were superconducting; this will maintain a magnetic field for as long as you keep it cool.

A conventional copper electromagnet continually loses energy through resistance, and this loss must be overcome to maintain  the magnetic field.

where does permanent magnet energy come from

Another way of looking at this question is that the "natural" state of the magnet's alloy has a very low external magnetic field (comparable to the Earth's magnetic field). So the same metal with a powerful magnetic field appears to be in a "higher energy" state.

This magnetization is imposed during magnet manufacture, by cooling it below the Curie temperature in the presence of a powerful external magnetic field.

But if you expose the magnet to environmental abuse: hitting it with a hammer, increasing its temperature near the Curie temperature, etc, then entropy means that the aligned magnetic domains will realign, and return to the inert state, matching Earth's weak magnetic field.

This is an effect of entropy - objects tend to return to a lower energy state.

Oops! Overlap with Bored Chemist...

[magistral (OP)]

Not sure about the metal spring analogy. I can see that in compresing a metal spring the applied force can cause that energy to be stored in the atoms of the metal and when you remove the force compressing the spring that energy can be used to return the spring to it's original shape. In the 2 magnets situation there is an air gap between them so where is the energy used to close the gap between the magnets stored in order to be used to reinstate the gap ?

[magistral (OP)]

'quote'
A conventional copper electromagnet continually loses energy through resistance, and this loss must be overcome to maintain  the magnetic field.

Are you saying that all the electrical energy supplied to an electromagnet is lost to resistance and none of it used to create the magnetic field ?

[evan_au]

Are you saying that all the electrical energy supplied to an electromagnet is lost to resistance and none of it used to create the magnetic field ?

It takes energy to create the strong magnetic field of a superconducting MRI magnet.
- There is no electrical resistance
- But the inductance means that you have to apply a voltage and a current to bring up the magnetic field: Volts x Amps x time = Energy
- Once the supercurrent is flowing, you don't need to apply any more energy to maintain it.

For a conventional copper DC electromagnet: Initially, energy goes into building the magnetic field.
- But once the current stabilizes, the magnetic field is constant
- All of the subsequent energy goes into resistance losses in the electromagnet, the power supply wires, or the power supply source.

[yor_on]

A very good question. And I think we can ignore how it gets placed in this configuration, as that was the intent of the question as I read it. The question of how this 'energy' acting against gravity keeps itself, and possibly what happens to it over time?
=

My own take on that one would be that this is a property, belonging to elementary particles as electrons. And in that motto, as we definite them as 'timeless' this property does not decay.

" All the experimental evidence we have (including evidence that the photon is massless) suggests that electric charge is conserved. So long as this conservation law holds, the electron will not decay. "

https://www.quora.com/Are-there-any-sub-atomic-particles-that-are-timeless-not-subject-to-any-form-of-decay-or-half-life

A 'field' is just the way this property gets expressed, as far as I get it. You can turn it around, expressing it as everything is a 'field' though, in where a electron becomes one of its manifestations. And where the logical conclusion from that perspective becomes one where this field must be 'timeless' too.

It doesn't really answer it, I know that, but that's as far as I can follow it through today. The next question should be what makes a property? And is that 'energy'?

You can think of it as although compositions of this 'timeless' field may be found to decay, as with different materials interacting, the singular composites creating it, the 'particles', does not decay. Well, possibly? And in that motto, also a question about what decoherence means here
=

some elemental particles can decay though, so I shouldn't have expressed it that way. And it's about something so esoteric as 'conservation laws' if it will be able to do so, quantum mechanics and 'tunnelings'.

https://www.quora.com/Why-do-particles-decay-1

It becomes very tricky to think of that electron as part of a field, as parts of that 'field' then can decay in some circumstances, with decay never being a timeless property. And the whole process should be quantum mechanical, shouldn't it? Then again, without a arrow of time there would be no probability at all. And thinking of it, neither would we find ideas as Feynman diagrams and time dilation's.

I'll add this one  https://profmattstrassler.com/articles-and-posts/particle-physics-basics/why-do-particles-decay/most-particles-decay-yet-some-dont/

Maybe a better way to express is to state that the composite creating a atom does not disappear although elements of it, as isotopes creating that atom, may change. In that motto all atoms I know of, even radioactive, should be 'timeless' too. and why some atoms acts that way? Wanting a lowest 'stable' (or at least semi stable) energy state? Another property of this universe. Those properties are weird, but they are what makes this universe exist.

https://hps.org/publicinformation/ate/faqs/atomsdecay.html

[Eternal Student]

Hi.

Are you @magistral still looking for discussion or is this thread too old now?

[magistral (OP)]

Over the years I have had many different answers to my question. However, I have never been totally convinced by the answers I got. Most of them quote text book Physics saying that there is no work done as nothing is moving ! If you have an explaination I would love to hear it.

[Kryptid]

Most of them quote text book Physics saying that there is no work done as nothing is moving !

That is correct. A table can hold a book up against the force of gravity, but it isn't doing any work. Same thing for the kind of magnetic levitation you are talking about.

[magistral (OP)]

Again, I don't like that analogy. The table is not compressable by the weight of the book. The air between my magnets is compressable by the weight of the upper magnet - and would be if the lower magnet were not there.

[Kryptid]

The table is not compressable by the weight of the book.

It is, actually. It's just so small that you can't see it with your eyes.

The air between my magnets is compressable by the weight of the upper magnet

You could do it in a vacuum and still get magnetic levitation, so the presence of air isn't relevant.

 

[Eternal Student]

Hi.

Most of them quote text book Physics saying that there is no work done as nothing is moving !

   and also this comment you (magistral) made in the first post:

Classical Physics seems to say that with the magnets in this static situation then no energy is involved and no work is done as
there is no movement or displacement.

    Seem to indicate that you already know that there is a difference between force and energy.   I'm going to try and avoid saying too much about that.
    There are already several good replies here that are telling you much the same things again.

- - - - -
     You have a situation with a magnetic field but if you just switched the words "magnetic field" and "magnetism" with the words "gravitational field" and "gravity",   then you'd probably accept the situation and never have bothered to question it.
    Let's have a go with this:
   Gravity exerts a force on me.   Today it's a force equal to my weight.  Tomorrow it will still be the same amount of force.   Gravity has acted on me all day long and yet the force has not reduced, it's not been depleted or leaked away at all.   The source of the gravitational field was the mass of the earth and unless some space aliens come along, mine the planet and fly off with most of it's mass then it jolly well should be the same mass as yesterday.   The source of gravity hasn't changed so the gravitational field hasn't changed, so the force I experience due to gravity did not change.
    Well, the same is happening with your magnets.   The upward force on the top magnet is due to the magnetic field.  The source of the magnetic field is the magnets and they don't change from day to day (they would if you bang the magnets about or heat them up too much but ordinarily they just stay magnetised in exactly the same way).   There is no reason to assume the force on the top magnet will ever fade way or get depleted,  just as you wouldn't have thought the force on you due to gravity will fade away tomorrow.

    So that's the static situation with the magnets explained.   The magnetic field is just like an unsusual gravitational field, this one pushes the top magnet upwards instead of pulling it downwards but other than that it's just like a gravitational field.   It never fades aways unless you change the source of that field.

    The situation where you were pushing the top magnet down is also very much like lifting an apple up in a gravitational field.  You are putting energy into the system (your hand is exerting a force and this gets moved through a distance which is the height you lift the apple, or the height you depress the top magnet).   You can imagine that this energy is stored temporarily in the field and is available later.  At school they probably called this "gravitational potential energy" for the gravitational field situation, they may not have given it a detailed name for magnetic fields but it is exactly the same sort of potential energy this one is just due to a different field.   The apple (or top magnet) will rapidly start to recover that potential energy from the field the moment you take your hand off it.  The apple (or magnet) will start to move (gain kinetic energy) as soon as you take your hand off it.  In the case of the magnetic field, the top magnet is accelerated upward.  In the case of the apple in the gravitational field it is accelerated downward.
    You can keep doing this as many times as you like.  Lift the apple up again tomorrow, and then let it go and check it has the same motion.  It will.  It will again the next day etc.   You're not taking any energy out of the system since you always had to put in that amount of energy when you lifted the apple up (or pushed the top magnet down).   Nothing changes, nothing leaks away.
    So that's the situation where you move the magnets.   You're just storing some extra energy in the field (for a while).  You don't take any more energy out of the field at the end then you put in yourself when you lifted the apple up (or pushed the magnet down).   So the whole field remains much the same at the end of it all, there's no overall energy change, no change in the sources of the field, no change in the field strength, no changes of any sort.

- - - - - -
   You went on to discuss electromagnets.   People have already provided some good answers for this.  Electromagnets don't maintain a constant magnetic field unless you keep the electrical power turned on.   This is different from the permanent magnets.

Best Wishes.

[evan_au]

there is no work done as nothing is moving

If you constrained the upper magnet so it just moved vertically on frictionless rails....
- You could push down on the upper magnet, and it would bounce up (past the neutral point), then fall down, bounce up, etc

There is still no work being done overall, because the potential energy is being exchanged for kinetic energy (and back again), so the energy of the system does not change.
- The motion is rapidly damped out, because there are lots of losses in this system: air resistance, eddy currents in the resistive iron-based magnets, etc (it works better with superconductors, but you still get losses).

The same type of motion happens with a weight hanging on a spring in a gravitational field (although the force on a spring is much more linear than the field of a typical magnet).

Oops! Overlap with Eternal Student...

[magistral (OP)]

Thanks guys for your excellent and detailed  replies.

I think I just need to get my head around the bit where  - energy is stored temporarily in the magnetic field.

[Eternal Student]

Hi again.

I think I just need to get my head around the bit where  - energy is stored temporarily in the magnetic field.

   
I'll just point out that what I actually said was:

You can imagine that this energy is stored temporarily in the field

     The idea of potential energy being stored in a field is just one simplified concept that is sometimes used.  It's not a bad idea either.  It is one good step closer to the truth and it's probably good enough for school.   However, when you're ready you can consider alternatives.    It's very much like teaching people about Newtonian mechanics first BEFORE you tell them that it's actually not quite right and start to teach them about Einstein and relativity.
     At the moment, yes,  I think it would be useful for you to consider that gravitational potential energy is stored in the gravitational field and that potential energy can be stored in the magnetic field in much the same way.

    There have been many other threads in this forum that discuss exactly what energy is (or isn't).  It's not straightforward.   At school most people will have the idea that energy is some sort of thing like a substance of some kind and it has to be "stored" somewhere.   Later on you might start developing other ideas about what energy is.

   I honestly don't know why I'm doing this.  I should just take the win, stop talking and walk away.  It's just that I have a lot of trouble saying simplified things and half-truths without making it clear that there are more advanaced theories and other ways of thinking about it. So that's what I'm doing here.   What I have presented is a simplified, good enough for school-level version of the way things are.

  So, yes, please do think that energy can be stored in a field like a magnetic field and a gravitational field.  That will be a good step forward.

Best Wishes.

[magistral (OP)]

Thanks for that. I will seek out the more advanced explanations !  Although I'm actually 76 years old, the school level explanation will suffice for now. 

[Eternal Student]

Hi again.

    Just to be clear,  where I've described something as being school-level I certainly didn't mean childish,  I just meant something which will be contested at University if you were studying in that area (studying Physics for example).

Best Wishes.

[hamdani yusuf]

Not sure about the metal spring analogy. I can see that in compresing a metal spring the applied force can cause that energy to be stored in the atoms of the metal and when you remove the force compressing the spring that energy can be used to return the spring to it's original shape. In the 2 magnets situation there is an air gap between them so where is the energy used to close the gap between the magnets stored in order to be used to reinstate the gap ?

In electronics, the analogy would be a capacitor. The energy here is stored in the form of electric charge density. When electrical energy is put into the capacitor, one plate will increase electron density, while the other will decrease it.
I guess something similar also happens in the your case with permanent magnets. Perhaps we can call it magnetic charge, although there is no material transfer involved here, AFAIK. Some microscopic changes might happen to those magnets when they are being compressed. We need some methods to detect these changes to settle this issue.

[Rocky6419]

Hi everyone, here I can tell you where the energy comes from in permanent magnets;
The energy from the permanent magnet comes because the electrons orbiting in one direction more than the others, and the electrons keep orbiting because nothing can interrupt them.